Seems really awkward and redundant to me. Who wants to pay for (or carry) a bag of 20 bricks when you could be buying a katana or ammo?
What would make sense though is using any physics object as a melee/thrown weapon in Killing Floor 2, with berserker getting a nice bonus to melee damage and throw range. I never played it myself, but I think there's a similar system in Dead Rising. It would have the feel of a survival game, when you are out of options and scrambling to pick anything up to defend yourself. And it would be nice for berserkers who happen to be standing in a pile of rubble to be able to crack some crawler skulls from a distance with a blunt object they found on the ground. If you have the free weight, you would be able to carry a smaller object like a brick in your inventory for later use, and pick it up afterwards if it doesn't break. Also, you could make traps by dropping heavy objects out of the windows on the second floor of the offices, for example.